Analysis of packet networks having contention-based reservation with application to GPRS

We develop a model to quantify the performance of message transmission systems in which users must reserve transmission resources via a contention mechanism prior to transmission. Our work is motivated by a desire to understand the performance characteristics of systems such as the general packet radio service (GPRS), where the single forward link of the wireless access system is organized as a sequence of frames, each of which has first a contention period and then a service period. There are a fixed number of fixed-length contention slots in each contention period. Each contending customer chooses at random the slot in which to contend, and success is determined by a capture model. A contender who fails waits for the next contention period, then again chooses at random the slot in which to contend; this process is repeated until the contender is successful. Customers who have contended successfully are served during the service period, which has a prescribed number of fixed-length slots, on a first-come-first-served (FCFS) basis, with the required number of service units being drawn independently from a general discrete distribution having finite support. We model the system as a Markov renewal process embedded at service departure times. We solve the model and then compute the equilibrium distributions of the number of customers in the system at arbitrary points in time and at customer arrival times. Finally, we give a numerical example in which we demonstrate the usefulness of our results in understanding the behavior of GPRS.